Since I don't have WiFi router and I don't have wire long enough for my arduino.So I'd like to ask if there it a device that one part is connected to router by cable and the other part is connected to arduino by cable too.The two parts are connected through their own wireless proctool? So my arduino can connected to Internet as if there is Wired Network(Ethernet).
This is probably not as inexpensive as you wanted, but I have used the Linksys WAP54G on the client end, and a WRT54G on the internet end for wire-to-wireless-to-wire links. It worked well, but it helps to be familiar with router setup and routing.
How far is the Arduino from the wired internet connection? That may help determine which devices will or will not work for you.
XBees seem ideally suited to your situation. Use an XBee on a XBee shield on the Arduino and an XBee on a USB Explorer at the PC end. The Series 1 models are simple to configure. Use is a matter of pretending that a real long serial cable is still connected.
Well, the simplest approach is to buy a wireless router, and either replace your current router, or plug the wireless router into the wired router. You would then use a wifi shield. I checked newegg.com (USA only) and you can get wireless routers for under $20, and at dealextreme (Asian reseller), for under $15. You should make sure the wireless router supports wifi b/g, as well as the new n protocols, since the wifi shield only seems to support b/g.
The secondary approach is to just get a longer ethernet cable. You can get 100' or 90m ethernet cables for under $20.
A third approach is to use a powerline ethernet adapter. You can buy a pair of these for around $40-50. You plug them into the wall socket, and one you connect to the router, and the other you connect to an Arduino using an ethernet shield. The networking is done over the power line.
I've got my arduino ethernet shield connected to my router using ~50'-60' of cat3 four conductor telephone wire and have no issues other than the conductors are solid and have broken at the RJ45 connector after flexing a lot.